量子代數(shù)U-,q-（f（K，K））的表示及其伴隨作用.pdf

1、河北師范大學(xué)碩士學(xué)位論文量子代數(shù)U（f（K，K））的表示及其伴隨作用姓名：孫秋媚申請學(xué)位級(jí)別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：張子龍20080320AbstractInthispaperletbasicfieldkiscomplexfieldC，Ndenotesthesetofnon—negativeintegers，Zdenotesthesetofpositiveintegers，letqbeaparameterwithqbeingnot

2、arootofunityBasedonquantumalgebras％(，(K))in【5】weconstructaalgebras％(，(K，K))：itisaassociativealgebrasgeneratedbyquadrupleE，EK，Ksatisfyingthefollowingrelations：KR=良K=J。KJ=K，kJ=露，KE=q2EK，kE=g一2E露，KF=q2FK，RE=q2FR，舊，F(xiàn)】=f(K，露)

3、=∑J∈No巧K‘影∈k[K，露】ItisgeneralizestheconditionKK一1=K一1K=1asKR=kg=Jwegivethenecessaryandsufficientconditionof％(，(K，K))haveastructureofweaknopfalgebraUnderthedefinitionofweakOreextensiondefinedbyLiFang，weprovethat％(廠(K，K))is

4、weakOreextensionofNoetherianringk[K，K】，SO％(，(K，K))isanoethenanringInthispaperwefindallfinitedimensionalintegrablehighestweight％(，(Ⅳ，Ⅸ))一module，itisformalasW(n)orK，nandwediscuss％(，(K，K))一module’SClebschGordanformula：(1)圪o

5、vb掣①答‘％∞圪6劃，(2)1吃oW(b)蘭(a1)w(6)，(3)W(b)圓K竺(a1)Ⅳ(6)，(4)W(a)oW(b)是平凡模Atlastweconstrasttoadjointactionforquantumalgebrawsl口(2)，weprovethat％(廠(K，K))isaleftquasi—modulealgebraoveritselfandstudythestructureofthesubmodulesof莎(％